Hello,
My post concerns the application of dominance analysis using Stata's -domin- command. I learned about it here.
Issue #1
I am using panel data on 56 countries over five years. I had initially intended to apply dominance analysis to a model that compares the relative importance of two independent variables - I'll call them Most Interesting Variable 1 (MIV1) and Most Interesting Variable 2 (MIV2). However, due to the highly correlated nature of MIV1 and MIV2, including them in the same regression is problematic.
So I have decided to split the model in two. In other words, I run a model as shown in eq(1) and a model as shown in eq(2), where Xjt is a vector of country-level macroeconomic factors. The regression is run using OLS. Country and year fixed effects are included and standard errors are clustered at the country-level. The only difference between these two models is that eq1 includes MIV1, while eq2 includes MIV2. The panel is balanced in both cases.
Yjt= β0 + β1MIV1jt + β2Xjt + δt + αj + uit (Eq1)
Yjt= β0 + β1MIV2jt + β2Xjt + δt + αj + uit (Eq2)
I will then run -domin- for each model (I plan on renting online space to run the models because of my inclusion of fixed effects will probably make this take very long). Because I am not interested in determining relative importance within each model for its own sake, but rather, interested in understanding the relative importance of MIV1 and MIV2, which are in separate models, I was planning to compare the standardised general dominance statistic for MIV1 from eq1 and the standardised dominance statistic for MIV2 from eq2 and to use their respective contributions to the within R-squared of each model to inform an assessment of their relative importance.
Question: Is it appropriate to compare the standardised general dominance statistics on two variables from different regressions, where these different regressions are identical in every respect except that one regression includes MIV1 and one includes MIV2? If not, and one just obtains coefficients from MIV2 and MIV2 as outputs for estimating two separate models, are there commonly accepted methods for comparing the relative importance of the coefficients across models? Simply comparing the size and statistical significance of MIV1 and MIV2, or the within R-squares of each model seems a bit naive.
Issue #2:
My dependent variable Yjt is serially correlated, which means the fixed effects OLS estimates are biased.
Question: If it is okay to use standardised general dominance statistics to compare the independent variables of interest between two models, and if one's research question is about determining relative importance between two independent variables using generalised dominance statistics, does the bias matter that much if this bias is 'consistent' between the two models?
Issue #3
Because Yjt is serially correlated, in addition to the static specification, I'd also like to run a specification that includes the lag of the dependent variable. For this, I have determined that systems GMM using -xtabond2- is most appropriate given my short T and N>T. However, to my understanding, this throws out the use of Dominance Analysis as an option to assess relative importance of MIV1 and MIV2 because -xtabond2- does not produce an appropriate fit-statistic.
Question: Is there a way that an -xtabond2- regression can be dominance analysed? If not, is there a procedure for comparing the relative importance of independent variables across two (almost) identical models in a dynamic panel setting? The short T and moderate N of my data constrain my options of dynamic panel data methods.
Thank you for taking the time to read this.
Sam
My post concerns the application of dominance analysis using Stata's -domin- command. I learned about it here.
Issue #1
I am using panel data on 56 countries over five years. I had initially intended to apply dominance analysis to a model that compares the relative importance of two independent variables - I'll call them Most Interesting Variable 1 (MIV1) and Most Interesting Variable 2 (MIV2). However, due to the highly correlated nature of MIV1 and MIV2, including them in the same regression is problematic.
So I have decided to split the model in two. In other words, I run a model as shown in eq(1) and a model as shown in eq(2), where Xjt is a vector of country-level macroeconomic factors. The regression is run using OLS. Country and year fixed effects are included and standard errors are clustered at the country-level. The only difference between these two models is that eq1 includes MIV1, while eq2 includes MIV2. The panel is balanced in both cases.
Yjt= β0 + β1MIV1jt + β2Xjt + δt + αj + uit (Eq1)
Yjt= β0 + β1MIV2jt + β2Xjt + δt + αj + uit (Eq2)
I will then run -domin- for each model (I plan on renting online space to run the models because of my inclusion of fixed effects will probably make this take very long). Because I am not interested in determining relative importance within each model for its own sake, but rather, interested in understanding the relative importance of MIV1 and MIV2, which are in separate models, I was planning to compare the standardised general dominance statistic for MIV1 from eq1 and the standardised dominance statistic for MIV2 from eq2 and to use their respective contributions to the within R-squared of each model to inform an assessment of their relative importance.
Question: Is it appropriate to compare the standardised general dominance statistics on two variables from different regressions, where these different regressions are identical in every respect except that one regression includes MIV1 and one includes MIV2? If not, and one just obtains coefficients from MIV2 and MIV2 as outputs for estimating two separate models, are there commonly accepted methods for comparing the relative importance of the coefficients across models? Simply comparing the size and statistical significance of MIV1 and MIV2, or the within R-squares of each model seems a bit naive.
Issue #2:
My dependent variable Yjt is serially correlated, which means the fixed effects OLS estimates are biased.
Question: If it is okay to use standardised general dominance statistics to compare the independent variables of interest between two models, and if one's research question is about determining relative importance between two independent variables using generalised dominance statistics, does the bias matter that much if this bias is 'consistent' between the two models?
Issue #3
Because Yjt is serially correlated, in addition to the static specification, I'd also like to run a specification that includes the lag of the dependent variable. For this, I have determined that systems GMM using -xtabond2- is most appropriate given my short T and N>T. However, to my understanding, this throws out the use of Dominance Analysis as an option to assess relative importance of MIV1 and MIV2 because -xtabond2- does not produce an appropriate fit-statistic.
Question: Is there a way that an -xtabond2- regression can be dominance analysed? If not, is there a procedure for comparing the relative importance of independent variables across two (almost) identical models in a dynamic panel setting? The short T and moderate N of my data constrain my options of dynamic panel data methods.
Thank you for taking the time to read this.
Sam